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arXiv:hep-ph/0703261v4 3 Oct 2007

Heavy neutrino signals at large hadron colliders

F. del Aguila1, J. A. Aguilar–Saavedra1, R. Pittau2

1 Departamento de F´ısica Te´orica y del Cosmos and CAFPE, Universidad de Granada, E-18071 Granada, Spain

2 Dipartimento di Fisica Teorica, Universit`a di Torino, and INFN Sezione di Torino, V. Pietro Giuria 1, I-10125 Torino, Italy

Abstract

We study the LHC discovery potential for heavy Majorana neutrino singlets in the process pp → W+→ ℓ+N → ℓ++jj (ℓ = e, µ) plus its charge conjugate.

With a fast detector simulation we show that backgrounds involving two like-sign charged leptons are not negligible and, moreover, they cannot be eliminated with simple sequential kinematical cuts. Using a likelihood analysis it is shown that, for heavy neutrinos coupling only to the muon, LHC has 5σ sensitivity for masses up to 200 GeV in the final state µ±µ±jj. This reduction in sensitivity, compared to previous parton-level estimates, is driven by the ∼ 102 − 103 times larger background. Limits are also provided for e±e±jj and e±µ±jj final states, as well as for Tevatron. For heavy Dirac neutrinos the prospects are worse because backgrounds involving two opposite charge leptons are much larger. For this case, we study the observability of the lepton flavour violating signal e±µjj. As a by-product of our analysis, heavy neutrino production has been implemented within the ALPGEN framework.

1 Introduction

Large hadron colliders involve strong interacting particles as initial states, giving rise to huge hadronic cross sections. The large luminosities expected will also provide quite large electroweak signals, with for instance 1.6 × 1010 (4 × 107) W bosons at LHC (Tevatron) for a luminosity of 100 (2) fb−1. Therefore, these colliders can be used for precise studies of the leptonic sector as well, and in particular they can produce new heavy neutrinos at an observable level, or improve present limits on their masses and mixings [1–4] (see Ref. [5] for a review). These new fermions transform trivially under the gauge symmetry group of the Standard Model (SM), and in the absence of other interactions they are produced and decay only through their mixing with the SM leptons. With new interactions, like for instance in left-right models [6], heavy neutrinos can be produced by gauge couplings unsuppressed by small mixing angles,

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yielding larger cross sections and implying a much higher collider discovery reach [7–10].

Heavy neutrinos could also be copiously produced in pairs through the exchange of a relatively light Z boson [11]. In these scenarios, however, the observation of the new interactions could be more interesting than the existence of new heavy neutrinos.

We will concentrate on the first possibility and neglect other new production mechan- ims, taking a conservative approach. In this case, for example, it has been claimed by looking at the lepton number violating (LNV) ∆L = 2 process pp(–)→ µ±µ±jj that LHC will be sensitive to heavy Majorana neutrinos with masses mN up to 400 GeV, whereas Tevatron is sensitive to masses up to 150 GeV [2, 4]. However, as we will show, taking into account the actual backgrounds these limits are far from being realistic. In par- ticular, backgrounds involving b quarks, including for instance t¯tnj (with nj standing for n = 0, 1, 2, . . . additional jets), are two orders of magnitude larger than previously estimated. Moreover, in the region mN < MW the largest and irreducible background is b¯bnj, by far dominant but overlooked in previous parton-level analyses [4]. In this work we make a detailed study, at the level of fast simulation, of the LHC sensitivity to Majorana neutrinos in the process pp → µ±µ±jj, which is the cleanest final state, for both mN > MW and mN < MW. We also study the processes pp → e±e±jj and pp → e±µ±jj for which the sensitivity is slightly worse. Heavy Dirac neutrinos do not produce LNV signals and then their observation is much more difficult. As an example, we examine the lepton flavour violating (LFV) signal e±µjj, produced by a heavy Dirac neutrino coupling to the electron and muon.

The generation of heavy neutrino signals has been implemented in the ALPGEN [12]

framework, including the process studied here as well as other final states. In the following, after making precise our assumptions and notation in section 2, we describe the implementation of heavy neutrino production in ALPGEN in section 3. We present our detailed results in section 4, where we will eventually find that heavy neutrinos can be discovered up to masses of the order of 200 GeV, and that for N lighter than the W boson its mixing can be probed at the 10−2 level (for a “reference” mass mN = 60 GeV). These figures are much less optimistic than in previous literature. Estimates for Tevatron are given in section 5, and our conclusions are drawn in section 6. In two appendices we detail the evaluation of the b¯bnj background and the heavy neutrino mass reconstruction, respectively.

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2 Heavy neutrino interactions

Our assumptions and notation are reviewed in more detail in Ref. [5] (see also Refs. [13, 14]). The SM is only extended with heavy neutrino singlets Nj, which are assumed to have masses of the order of the electroweak scale, up to few hundreds of GeV. We concentrate on the lightest one, assuming for simplicity that the other extra neutrinos are heavy enough to neglect possible interference effects. The new heavy neutrino N (where we suppress the unnecessary subindex) can have Dirac character, what requires the addition of at least two singlets, or Majorana, in which case (NL)c ≡ CNLT = NR

and lepton number is violated. In either case it is produced and decays through its mixing with the light leptons, which is described by the interaction Lagrangian (in standard notation)

LW = − g

√2

ℓγ¯ µVℓNPLN Wµ+ ¯NγµVℓN PLℓ Wµ , LZ = − g

2cW

¯

νγµVℓNPLN + ¯N γµVℓN PLν Zµ, LH = −g mN

2MW

¯

νVℓNPRN + ¯N VℓN PLν H . (1) The SM Lagrangian remains unchanged in the limit of small mixing angles VℓN, ℓ = e, µ, τ (which is the actual case), up to very small corrections O(V2). Neutral couplings involving two heavy neutrinos are also of order V2. The heavy neutrino mass mN joins two different bispinors in the Dirac case and the same one in the Majorana case. Heavy neutrino decays are given by their interactions in Eqs. (1): N → W+, N → Zν, N → Hν, plus N → W+ for a heavy Majorana neutrino. For mN < MW all these decays produce three body final states, mediated by off-shell W , Z or H bosons. The total width for a Majorana neutrino is twice larger than for a Dirac one with the same couplings [5, 15–17].

As it is apparent from Eqs. (1), heavy neutrino signals are proportional to the neutrino mixing with the SM leptons VℓN. Limits on these matrix elements have been extensively discussed in previous literature, and we quote here only the main results.

Low-energy data constrain the quantities

ℓℓ ≡ δℓℓ

3

X

i=1

VℓνiVνi =

n

X

j=1

VℓNjVNj. (2)

A global fit to tree level processes involving light neutrinos as external states gives [18, 19],

ee≤ 0.0054 , Ωµµ ≤ 0.0096 , Ωτ τ ≤ 0.016 (3)

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at 90% confidence level (CL). Note that a global fit without the unitarity bounds implies Ωee ≤ 0.012 [18]. Additionally, for Majorana neutrinos coupling to the electron the experimental bound on neutrinoless double beta decay requires [20]

n

X

j=1

VeN2 j 1 mNj

< 5 × 10−8 GeV−1. (4)

If VeNj saturate Ωee in Eq. (3), this limit can be satisfied either demanding that mNj

are large enough, beyond the TeV scale [21] and then beyond LHC reach, or that there is a cancellation among the different terms in Eq. (4), as may happen in definite models [22], in particular for (quasi)Dirac neutrinos.

Flavour changing neutral processes further restrict Ωℓℓ. The new contributions, and then the bounds, depend on the heavy neutrino masses. In the limit m2Nj ≫ MW2

|VℓNj|2m2Nj 1 they imply [24]

|Ω| ≤ 0.0001 , |Ω| ≤ 0.01 , |Ωµτ| ≤ 0.01 . (5) Except in the case of Ω, for which experimental constraints on lepton flavour violation are rather stringent, these limits are similar to the limits on the diagonal elements. An important difference, however, is that (partial) cancellations among loop contributions of different heavy neutrinos may be at work [25]. Cancellations with other new physics contributions are also possible. Since we are interested in determining the heavy neu- trino discovery potential and the direct limits on neutrino masses and mixings which can be eventually established, we must consider the largest possible neutrino mixings, although they may require model dependent cancellations or fine-tuning.

3 Heavy neutrino production with ALPGEN

For the signal event generation we have extended ALPGEN [12] with heavy neutrino production. This Monte Carlo generator evaluates tree level SM processes and provides unweighted events suitable for simulation. A simple way of including new processes taking advantage of the ALPGEN framework is to provide the corresponding squared amplitudes decomposed as a sum over the different colour structures. In the case of heavy neutrinos this is trivial because there is only one term. This method requires to evaluate from the beginning the squared amplitudes for the processes one is interested

1When VℓNj > MW/mNj the non-decoupling terms in the amplitude, proportional to VℓN4jm2Nj/MW2 , cannot be neglected because they dominate over the VℓN2j terms [23].

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in, what is done using HELAS [26]. An alternative possibility which gives more flexi- bility for future applications is to implement the new vertices at the same level as the SM ones, what is quite more involved.

We have restricted ourselves to single heavy neutrino production. Pair production is suppressed by an extra V2 mixing factor and by the larger center of mass energy required, what implies smaller PDFs and more suppressed s-channel propagators. Sin- gle heavy neutrino production can proceed through s-channel W, Z or H exchange.

The first two production mechanisms have been implemented in ALPGEN for the var- ious possible final states given by the heavy neutrino decays N → W±, N → Zν, N → Hν with ℓ = e, µ, τ , and for both Dirac or Majorana N. In the case mN < MW

all decays are three-body, and mediated by off-shell W , Z or H. The transition from two-body to three-body decays on the MW, MZ and MH thresholds is smooth, since the calculation of matrix elements and the N width are done for off-shell intermediate bosons. Two approximations are made, however. The small mixing of heavy neu- trinos with charged leptons implies that their production is dominated by diagrams with N on-shell, like those shown in Fig. 1, with a pole enhancement factor, and that non-resonant diagrams are negligible. (Additionally, to isolate heavy neutrino signals from the background one expects that the heavy neutrino mass will have to be recon- structed to some extent.) Then, the only diagrams included are the resonant ones. In the calculation we also neglect light fermion masses except for the bottom quark.

q q

W N

W

()

ℓ q

q

W N

W+

()

(a) (b)

Figure 1: Feynman diagrams for the process q ¯q → ℓ+N, followed by LNV decay N → ℓ()+W (a) and lepton number conserving (LNC) decay N → ℓ()−W+ (b). The diagrams for the charge conjugate processes are similar.

Generator-level results are presented in Fig. 2 for LHC and Tevatron in the relevant mass ranges. Solid lines correspond to the total µN cross sections for |VµN| = 0.098, VeN = Vτ N = 0. The dashed lines are the cross sections for the final state µ±µ±jj,

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which is the cleanest one. The dotted lines are the same but with kinematical cuts LHC : pµT ≥ 10 GeV , |ηµ| ≤ 2.5 , ∆Rµj ≥ 0.4 ,

pjT ≥ 10 GeV , |ηj| ≤ 2.5 ,

Tevatron : pµT ≥ 10 GeV , |ηµ| ≤ 2 , ∆Rµj ≥ 0.4 ,

pjT ≥ 10 GeV , |ηj| ≤ 2.5 , (6)

included to reproduce roughly the acceptance of the detector and give approximately the “effective” size of the observable signal. Of course, the correct procedure is to per- form a simulation, as we do in next section, but for illustrative purposes we include the cross-sections after cuts. In particular, they clearly show that although for mN < MW

the total cross sections grow several orders of magnitude, both at LHC and Tevatron, partons tend to be produced with low transverse momenta (the two muons and two quarks result from the decay of an on-shell W ), making the observable signal much smaller. These results are in agreement with those previously obtained in Ref. [4].

40 60 80 100 120 140 160 180 200

mN 10-3

10-2 10-1 1 10 102

σ (pb)

N production µ±µ±jj µ±µ±jj with cuts

LHC

40 50 60 70 80 90 100 110 120 130 140

mN 10-4

10-3 10-2 10-1 1 10

σ (pb)

N production µ±µ±jj µ±µ±jj with cuts

Tevatron

Figure 2: Cross sections for heavy neutrino production at LHC (left) and Tevatron (right), as a function of the heavy neutrino mass, for |VµN| = 0.098. The solid lines correspond to total µN cross section, the dashed lines include the decay to like-sign muons and the dotted lines are the same but including the kinematical cuts in Eq. (6).

4 Di-lepton signals at LHC

The most interesting scenario for LHC is when the heavy neutrino has Majorana nature and couples only to the muon, so that it produces a final state µ±µ±jj with two same sign muons and at least two jets. Since this LNV signal has sometimes been considered [2,4] to be almost background free (more realistic background estimates are given in Ref. [27]), a detailed discussion of the actual backgrounds is worthwhile. A

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first group of processes involves the production of additional leptons, either neutrinos or charged leptons (which may be missed in the detector). The main ones are W±W±nj and W±Znj. We point out that not only the processes with n = 2 contribute: processes with n < 2 are backgrounds due to the appearance of extra jets from pile-up, and processes with n > 2 cannot be cleanly removed because of pile-up on the signal. A second group includes final states with b and/or ¯b quarks, like t¯tnj, with semileptonic decay of the t¯t pair, and W b¯bnj, with W decaying leptonically. In these cases the additional like-sign muon results from the decay of a b or ¯b quark. Only a tiny fraction of such decays produce isolated muons with sufficiently high transverse momentum.

But, since the t¯tnj and W b¯bnj cross sections are so large, these backgrounds are also much larger than backgrounds with two weak gauge bosons. Finally, b¯bnj production is several orders of magnitude larger than all processes mentioned above, but the produced muons have small pT and invariant mass in this case. Then, in general it might be eliminated with suitable high-pT cuts on charged leptons [28] (see section 4.1), but for mN < MW the heavy neutrino signal is also characterised by very small transverse momenta (see section 4.2), and this background turns out to be the dominant one.

The same applies for c¯cnj, but with the difference that c quark decays produce isolated charged leptons much less often than b decays.

Other LNV signals produced by heavy neutrinos are e±e±jj and e±µ±jj. They have the same SM backgrounds but with one important difference: b decays produce

“apparently isolated” electrons more often than muons, because electrons are detected in the calorimeter while muons travel to the muon chamber. Hence, the correspond- ing backgrounds t¯tnj, b¯bnj → e±e±X/e±µ±X are larger than the ones involving only muons. A precise evaluation of these backgrounds, optimising the criteria for electron isolation, seems to require a full simulation of the detector. The limits provided in these cases must be regarded with some caution in this respect, and should be confirmed with a full detector simulation.

We have generated the signal and backgrounds using ALPGEN and passing them through PYTHIA 6.4 [29] with the MLM prescription [30] to avoid double counting of jet radiation. A fast simulation of the ATLAS detector [31] has been performed. For the signal and all backgrounds except b¯bnj and c¯cnj the number of simulated events corresponds to at least 10 times the luminosity considered (which is 30 fb−1), so as to reduce statistical fluctuations, and the number of events is scaled accordingly. For b¯bnj and c¯cnj the luminosity simulated is 0.075 fb−1. Their evaluation is further discussed in appendix A. It must also be noted that in the signal simulation all W decays in pp → ℓN → ℓℓW are included. Leptonic W decays give an extra ∼ 20% contribution to di-lepton final states when the charged lepton from the W decay is missed, or when

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W decays to τ ν and the tau lepton decays hadronically.

4.1 ℓ

±

±

jj production for m

N

> M

W

In this mass region we take the reference values mN = 150 GeV and (a) VµN = 0.098, VeN = Vτ N = 0; (b) VeN = 0.073, VµN = Vτ N = 0; (c) VeN = 0.073, VµN = 0.098, Vτ N = 0. The pre-selection criteria used for our analysis are:

(i) two like-sign isolated charged leptons with pseudorapidity |η| ≤ 2.5 and trans- verse momentum pT larger than 10 GeV (muons) or 15 GeV (electrons), and no additional isolated charged leptons;

(ii) no additional non-isolated muons;

(iii) two jets with |ηj| ≤ 2.5 and pjT ≥ 20 GeV.

We point out that for µ±µ±jj final states the requirement (ii) reduces the backgrounds involving Z bosons by almost a factor of two, and thus proves to be quite useful.

The number of events at LHC for 30 fb−1 after pre-selection cuts is given in Table 1.

Additional backgrounds such as t¯b, t¯tt¯t, t¯tb¯b, Zt¯tnj, W W Znj, W ZZnj and ZZZnj are smaller and we do not show them, but they are included in the estimation of the signal significance below. The number of like-sign dimuon events from c¯cnj displayed between parentheses corresponds to an estimation, because no µ±µ±X events are found in the sample simulated (more details can be found in appendix A). We also note that the higher pT threshold for electrons contributes to the difference between the numbers of e±e±jj and µ±e±jj events, which are expected to be similar in some cases, for example for t¯tnj.

Let us concentrate on µ±µ±jj final states. The fast simulation shows that SM backgrounds are about two orders of magnitude larger than previously estimated (three orders if we include b¯bnj). Moreover, they cannot be sufficiently suppressed with respect to the heavy neutrino signal using simple cuts. Some obvious discriminating variables are:

• The missing momentum p6T. It is smaller for the signal because it does not have neutrinos in the final state, but nonzero due to energy mismeasurement in the detector.

• The separation between the muon with smallest pT (we label the two muons as µ1, µ2, by decreasing transverse momentum) and the closest jet, ∆Rµ2j. For backgrounds involving high-pT b quarks this separation tends to be rather small.

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Pre-selection Selection µ±µ± e±e± µ±e± µ±µ± e±e± µ±e±

N (a) 113.6 0 0 59.1 0 0

N (b) 0 72.0 0 0 17.6 0

N (c) 78.4 25.5 82.6 41.6 4.7 22.4

b¯bnj 14800 52000 82000 0 0 0

c¯cnj (11) 300 200 (0) 0 0

t¯tnj 1162.1 8133.0 15625.3 2.4 8.3 7.7

tj 60.8 176.5 461.5 0.0 0.0 0.1

W b¯bnj 124.9 346.7 927.3 0.4 0.6 0.3

W t¯tnj 75.7 87.2 166.9 0.3 0.0 0.0

Zb¯bnj 12.2 68.9 117.0 0.0 0.2 0.0

W W nj 82.8 89.0 174.8 0.5 0.1 0.7

W Znj 162.4 252.0 409.2 4.8 1.8 2.3

ZZnj 3.8 13.3 12.9 0.0 0.6 0.1

W W W nj 31.9 30.1 64.8 0.9 0.1 0.0

Table 1: Number of ℓ±±jj events at LHC for 30 fb−1, at the pre-selection and selection levels. The heavy neutrino signal is evaluated assuming mN = 150 GeV and coupling (a) to the muon, VµN = 0.098; (b) to the electron, VeN = 0.073; (c) to both, VeN = 0.073 and VµN = 0.098.

• The transverse momentum of the two muons, pµT1 and pµT2, respectively. In par- ticular pµT2 is a good discriminant against backgrounds from b quarks, because these typically have one muon with small pT.

These variables are plotted in Fig. 3 for the µ±µ±jj signal and the backgrounds grouped in three classes with common features: (a) b¯bnj, where both muons come from b quark decays (the contribution of c¯cnj is negligible); (b) t¯tnj, tj and W/Zb¯bnj, where one muon comes from a b quark; (c) backgrounds where both muons come from W/Z decays (mainly di-boson and tri-boson production). Kinematical cuts on the variables listed above do not render the µ±µ±jj final state “background free”, as it is apparent from the plots (and we have explicitly checked). Indeed, for the large background cross sections in Table 1 the overlapping regions contain a large number of background events, and they can be eliminated only by severely reducing the signal. However, a likelihood analysis using these and further variables can efficiently reduce the background. The additional variables are shown in Fig. 4:

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0 20 40 60 80 100 120 140 160 180 200 p/T

0 0.05 0.10 0.15 0.20 0.25 0.30

Fraction of events / 5 GeV

N (150) bbnj SM bkg (b) SM bkg (no b)

0 1 2 3 4

∆Rµ

2j 0

0.05 0.10 0.15 0.20 0.25 0.30

Fraction of events / 0.2

N (150) bbnj SM bkg (b) SM bkg (no b)

0 20 40 60 80 100 120 140 160 180 200

pTµ1 0

0.1 0.2 0.3 0.4 0.5 0.6

Fraction of events / 5 GeV

N (150) bbnj SM bkg (b) SM bkg (no b)

0 20 40 60 80 100 120 140

pTµ2 0

0.2 0.4 0.6 0.8 1.0

Fraction of events / 5 GeV

N (150) bbnj SM bkg (b) SM bkg (no b)

Figure 3: Normalised distributions of several discriminating variables for the µ±µ±jj signal with mN = 150 GeV and its backgrounds (see the text).

• The invariant mass mjj of the two jets with largest transverse momentum, which for the signal are assumed to originate from the W hadronic decay, and the invariant mass of µ2(the muon with lowest pT) and these two jets, mW µ2. (Further details about the W and N mass reconstruction can be found in appendix B.) An important observation in this case is that in backgrounds involving b quarks this muon typically has a small pT, displacing the background peaks to lower invariant masses.

• The invariant mass of the two muons.

• The separation between the muon with largest pT and the closest jet, ∆Rµ1j.

• The number of b-tagged jets Nb and jet multiplicities Nj. Especially the former helps to separate the backgrounds involving b quarks because they often have b- tagged jets. In this fast simulation analysis we have fixed the b-tagging efficiency to 60%, but in a full simulation the b tag probability can be included in the likelihood function, improving the discriminating power of this variable.

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0 50 100 150 200 250 300 350 mjj

0 0.05 0.10 0.15

Fraction of events / 5 GeV

N (150) bbnj SM bkg (b) SM bkg (no b)

0 50 100 150 200 250 300

m

2

0 0.05 0.10 0.15 0.20

Fraction of events / 5 GeV

N (150) bbnj SM bkg (b) SM bkg (no b)

0 100 200 300 400

mµµ 0

0.1 0.2 0.3 0.4

Fraction of events / 10 GeV

N (150) bbnj SM bkg (b) SM bkg (no b)

0 1 2 3 4

∆Rµ

1j 0

0.05 0.10 0.15 0.20

Fraction of events / 0.2

N (150) bbnj SM bkg (b) SM bkg (no b)

0 1 2 3 4 5

Nb 0

0.2 0.4 0.6 0.8 1

Fraction of events

N (150) bbnj SM bkg (b) SM bkg (no b)

0 5 10 15

Nj 0

0.1 0.2 0.3 0.4 0.5 0.6

Fraction of events

N (150) bbnj SM bkg (b) SM bkg (no b)

0 50 100 150 200 250 300

pTmax 0

0.1 0.2 0.3 0.4 0.5

Fraction of events / 10 GeV

N (150) bbnj SM bkg (b) SM bkg (no b)

0 20 40 60 80 100 120

pTmax2 0

0.2 0.4 0.6 0.8

Fraction of events / 5 GeV

N (150) bbnj SM bkg (b) SM bkg (no b)

Figure 4: Normalised distributions of several discriminating variables for the µ±µ±jj signal with mN = 150 GeV and its backgrounds (see the text).

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• The transverse momenta of the two jets with largest pT, pmaxT and pmax2T respec- tively.

These variables are not suited for performing kinematical cuts but greatly improve the discriminating power of a likelihood function. The resulting log-likelihood function is also shown in Fig. 5, where we distinguish four likelihood classes as in the previous figures: the signal, b¯bnj, backgrounds with one muon from b decays, and backgrounds with both muons from W/Z decays.

-10 -5 0 5 10

log10LS / LB 0

0.02 0.04 0.06 0.08

Fraction of events

N (150) bbnj SM bkg (b) SM bkg (no b)

Figure 5: Log-likelihood function for the µ±µ±jj signal with mN = 150 GeV and its backgrounds.

The probability distributions built for µ±µ±jj final states are used for e±e±jj and µ±e±jj as well. As selection criteria we require log10LS/LB ≥ 1.4 for µ±µ±jj and log10LS/LB ≥ 2.5 for e±e±jj and µ±e±jj final states, respectively, and that at least one of the two heavy neutrino mass assignments mW µ1, mW µ2 is between 130 and 170 GeV.2 The number of events surviving these cuts can be read on the right part of Table 1. As it is apparent, the likelihood analysis is quite effective in suppressing backgrounds, especially b¯bnj, t¯tnj and W/Zb¯bnj. The resulting statistical significance for the heavy neutrino signals are collected in Table 2, assuming a “reference” 20%

systematic uncertainty in the backgrounds (which still has to be precisely evaluated in a dedicated study). The limits on heavy neutrino masses and couplings depend on the light lepton they are coupled to. We can consider two extreme cases:

(a) A 150 GeV heavy neutrino coupling only to the muon can be discovered for

2The latter requirement assumes a previous knowledge of mN. In the same way, the signal distri- butions for the likelihood analysis must be built for a fixed mN value. Thus, experimental searches must be performed by comparing data with Monte-Carlo samples generated for different values of mN. This procedure, although more involved than a search with generic cuts, provides much better sensitivity.

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µ±µ± e±e± µ±e±

N (a) 16.2σ − −

N (b) − 4.2σ −

N (c) 11.4σ 1.1σ 5.5σ

Table 2: Statistical significance of the heavy neutrino signals in the different channels, for a mass mN = 150 GeV and coupling (a) to the muon, VµN = 0.098; (b) to the electron, VeN = 0.073; (c) to both, VeN = 0.073 and VµN = 0.098.

mixings |VµN| ≥ 0.054, and if no background excess is found the limits |VµN|2 ≤ 0.97 (1.2) × 10−3 can be set at 90% (95%) CL, improving the ones from low energy processes (see section 2) by a factor of 10. Heavy neutrino masses up to 200 GeV can be observed with 5σ at the LHC for VµN = 0.098.

(b) A 150 GeV heavy neutrino coupling only to the electron can be discovered for mixings |VeN| ≥ 0.080 (excluded by the limits in section 2), but if no background excess is found the limits |VeN|2 ≤ 2.1 (2.5) × 10−3, which are slightly better than the one derived from Eq. (3), can be set at 90% (95%) CL. Heavy neutrino masses up to 145 GeV can be observed with 5σ at the LHC for VeN = 0.073.

For a heavy neutrino coupling to the electron and muon the limits depend on both couplings as well as on its mass. The combined limits for mN = 150 GeV are displayed in Fig. 6. Except in the regions with VeN ∼ 0 or VµN ∼ 0, the indirect limit from µ − e LFV processes, also shown in this plot, is much more restrictive.

These limits can be considered conservative in the sense that only the lowest-order signal contribution (without hard extra jets at the partonic level) has been included, and further signal contributions ℓNnj should improve the heavy neutrino observability.

If the Higgs is heavier than 120 GeV the branching ratios Br(N → W ℓ) will increase as well. We also stress again that in the e±e±jj and µ±e±jj channels the evaluation of t¯tnj and other backgrounds with isolated electrons from b quarks must be confirmed with a full simulation, with an eventual optimisation of the isolation criteria. This is beyond the scope of the present work.

It is worth explaining here in more detail why our results are much more pes- simistic than previous ones. With this purpose, we apply to signal and backgrounds the sequential kinematical cuts in Ref. [4]:

• Missing energy p6T < 25 GeV.

• Lego-plot separation ∆Rµj > 0.5.

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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 VeN

0 0.02 0.04 0.06 0.08

VµN

Significance < 5σ 90% CL limit Indirect bound

Figure 6: Combined limits on VeN and VµN, for Vτ N = 0 and mN = 150 GeV. The red areas represent the 90% CL limits if no signal is observed. The white areas correspond to the region where a combined statistical significance of 5σ or larger is achieved. The indirect limit from µ − e LFV processes is also shown.

• Dijet invariant mass 60 GeV < mjj < 100 GeV, where the two jets are expected to come from the W boson in the case of the signal.

The number of events for the signal and main backgrounds after these cuts are gathered in the left column of Table 3 (we do not show smaller backgrounds for brevity). For mN = 150 GeV and VµN = 0.098 the signal cross section is reduced to 1.7 fb, to be compared to ∼ 2.2 fb in Ref. [4]. But our total background cross section after cuts amounts to 44 fb, while their estimate is of 0.04 fb. This difference by a factor of 1000 arises mainly from the b¯bnj background, overlooked before, which is by far the largest one. But even if b¯bnj is not taken into account, the background cross section ∼ 0.88 fb is 20 times larger, due to: (i) t¯tnj, which was assumed negligible after cuts, and W/Zb¯bnj, also overlooked; (ii) the W Znj background, because parton-level analyses underestimate the probability of missing a lepton and thus its contribution; (iii) pile-up, which makes lower order processes (n < 2) contribute. All these backgrounds, collected in Table 3, can be compared to W W W , which was found to be the main background before. The resulting statistical significance of the signal, ignoring systematic errors, is S/√

B = 1.41σ for 30 fb−1, far from the ∼ 30σ previously estimated. (If one makes the more realistic assumption that systematic errors are of order 20%, as we do in this work, then the statistical significance is further reduced to 0.19σ.) It could be argued that the cuts in the previous list might be strengthened in order to further reduce the backgrounds. But this would be at the cost of reducing the signal as well. On the other hand, additional cuts on lepton transverse momenta can be introduced to reduce b¯bnj and t¯tnj. Requiring that one charged lepton has pT ≥ 30 GeV and the other

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one pT ≥ 20 GeV, the signal is hardly affected while b¯bnj is essentially eliminated, as it is shown in the second column of Table 3. The statistical significance in this case is S/√

B = 14.1σ (ignoring systematic errors) or 12.1σ (with 20% systematics). We emphasise that, as it can be observed by comparing Tables 1 and 3, a probabilistic analysis is much more powerful in this case than a standard one based on cuts. But at any rate recovering parton-level estimates for the signal significance seems hardly possible.

Sequential cuts I Sequential cuts II

N (µ) 51.3 44.0

b¯bnj 1293 2.7

t¯tnj 15.3 1.4

W b¯bnj 3.6 0.2

W t¯tnj 0.7 0.7

Zb¯bnj 0.9 0.0

W W nj 0.5 0.5

W Znj 4.1 2.9

W W W nj 1.1 0.9

Table 3: Number of µ±µ±jj events at LHC for 30 fb−1, after the kinematical cuts in Ref. [4] (first column) and with additional requirements (second column, see the text).

The heavy neutrino signal is evaluated assuming mN = 150 GeV and VµN = 0.098.

Finally, we would like to note that we have not addressed the observability of heavy neutrino signals in τ lepton decay channels because they are expected to have much worse sensitivity. For hadronic τ decays the charge of the decaying lepton seems rather difficult to determine, hence backgrounds from top pair and Z production will be huge (see also section 4.3 below). For leptonic decays τ → ℓντ¯ν, ℓ = e, µ, not only the branching ratios are smaller, but also the signal has final state neutrinos and thus the discriminating power of p6 T against di-boson and tri-boson backgrounds is much worse.

4.2 ℓ

±

±

jj production for m

N

< M

W

In this mass region we take the reference values mN = 60 GeV and (a) VµN = 0.01, VeN = Vτ N = 0; (b) VeN = 0.01, VµN = Vτ N = 0; (c) VeN = 0.01, VµN = 0.01, Vτ N = 0. The pre-selection criteria are the same as before. The likelihood analysis is performed distinguishing four classes: the signal, b¯bnj, backgrounds with one muon from b decays, and backgrounds with both muons from W/Z decays. The relevant

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variables are depicted in Figs. 7 and 8:

• The transverse momenta of the two muons (slightly smaller for b¯bnj than for the signal, and much larger for the other backgrounds).

• The distance between them and the closest jet, which is a good discriminator against t¯tnj but not against b¯bnj.

• The rapidity difference between the muons and the W from N decay, which is reconstructed from the two jets with highest pT.

• The transverse momenta of the two jets with largest pT. Again, these two vari- ables are excellent discriminators against high-pT backgrounds like t¯tnj and di- boson production, but not very useful for b¯bnj.

• The missing transverse momentum.

• The invariant mass of the two muons and two jets with highest pT, mµµjj. For the signal, these four particles result from the decay of an on-shell W boson, so the distribution is very peaked around 100 GeV (the position of the peak is displaced as a consequence of pile-up, which generates jets with larger pT than the ones from the signal itself). Unfortunately, for b¯bnj the distribution is quite similar.

• The number of b tags and the jet multiplicity.

• The azimuthal angle (in transverse plane) between the two muons, φµµ. For b¯b without additional jets this angle is often close to 180, but for b¯bj and higher order processes (which are also huge) this no longer holds.

The resulting log-likelihood function is presented in Fig. 8. As it can be easily noticed with a quick look at the variables presented, the kinematics of b¯bnj is very similar to the signal and so this background is very difficult to eliminate. In particular, for larger mN requiring large transverse momentum for the leptons drastically reduces b¯bnj (as seen in the previous subsection), but for mN < MW it reduces significantly the signal as well. As selection cut we require log10LS/LB ≥ 2.2 for the three final states, which practically eliminates all backgrounds except b¯bnj. The number of remaining background events is given in the right part of Table 4 (numbers of background events at pre-selection equal those in Table 1, and are quoted on the left for better comparison).

Requiring larger LS/LB for the e±e±jj and µ±e±jj channels does not improve the results, because it decreases the signals too much. The resulting statistical significance

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0 20 40 60 80 100 120 pTµ1

0 0.1 0.2 0.3 0.4 0.5 0.6

Fraction of events / 5 GeV

N (60) bbnj SM bkg (b) SM bkg (no b)

0 20 40 60 80

pTµ2 0

0.2 0.4 0.6 0.8 1.0

Fraction of events / 5 GeV

N (60) bbnj SM bkg (b) SM bkg (no b)

0 1 2 3 4

Rµ

1j 0

0.05 0.10 0.15 0.20

Fraction of events / 0.2

N (60) bbnj SM bkg (b) SM bkg (no b)

0 1 2 3 4

Rµ

2j 0

0.05 0.10 0.15 0.20 0.25 0.30

Fraction of events / 0.2

N (60) bbnj SM bkg (b) SM bkg (no b)

0 1 2 3 4 5

|∆η

1

| 0

0.05 0.10 0.15 0.20

Fraction of events / 0.2

N (60) bbnj SM bkg (b) SM bkg (no b)

0 1 2 3 4 5

|∆η

2

| 0

0.05 0.10 0.15

Fraction of events / 0.2

N (60) bbnj SM bkg (b) SM bkg (no b)

0 50 100 150 200 250 300

pTmax 0

0.1 0.2 0.3 0.4 0.5

Fraction of events / 10 GeV

N (60) bbnj SM bkg (b) SM bkg (no b)

0 20 40 60 80 100 120

pTmax2 0

0.2 0.4 0.6 0.8

Fraction of events / 5 GeV

N (60) bbnj SM bkg (b) SM bkg (no b)

Figure 7: Normalised distributions of several discriminating variables for the mN = 60 GeV signal and the three background classes (see the text).

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0 20 40 60 80 100 120 140 160 180 200 p/T

0 0.05 0.10 0.15 0.20 0.25 0.30

Fraction of events / 5 GeV

N (60) bbnj SM bkg (b) SM bkg (no b)

0 100 200 300 400 500 600 700 800

mµµjj 0

0.05 0.10 0.15 0.20 0.25

Fraction of events / 10 GeV

N (60) bbnj SM bkg (b) SM bkg (no b)

0 1 2 3 4 5

Nb 0

0.2 0.4 0.6 0.8 1

Fraction of events

N (60) bbnj SM bkg (b) SM bkg (no b)

0 5 10 15

Nj 0

0.1 0.2 0.3 0.4 0.5 0.6

Fraction of events

N (60) bbnj SM bkg (b) SM bkg (no b)

-1 -0.5 0 0.5 1

cos ∆φµµ 0

0.1 0.2 0.3 0.4 0.5

Fraction of events / 0.1

N (60) bbnj SM bkg (b) SM bkg (no b)

-10 -5 0 5

log10LS / LB 0

0.02 0.04 0.06 0.08

Fraction of events

N (60) bbnj SM bkg (b) SM bkg (no b)

Figure 8: Normalised distributions of several discriminating variables for the mN = 60 GeV signal and the three background classes (see the text). The last plot corresponds to the log-likelihood function.

for the heavy neutrino signals are collected in Table 5, assuming a 20% systematic uncertainty in the backgrounds. From these significances, the following limits can be extracted:

(a) A 60 GeV neutrino coupling only to the muon can be discovered for mixings

|VµN| ≥ 0.0070, and bounds |VµN|2 ≤ 1.65(1.95) × 10−5 can be set at 90% (95%) CL if a background excess is not observed. These figures are ∼ 35 times worse than in previous parton-level estimates which overlooked the main background

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Pre-selection Selection µ±µ± e±e± µ±e± µ±µ± e±e± µ±e±

N (a) 427.3 0 0 42.1 0 0

N (b) 0 174.7 0 0 33.9 0

N (c) 214.0 88.5 290.9 20.4 17.1 39.3

b¯bnj 14800 52000 82000 10.7 291 96

c¯cnj (11) 300 200 (0) 0 0

t¯tnj 1162.1 8133.0 15625.3 0.3 1.3 1.3

tj 60.8 176.5 461.5 0.0 0.0 0.1

W b¯bnj 124.9 346.7 927.3 0.2 2.4 1.3

W t¯tnj 75.7 87.2 166.9 0.0 0.0 0.0

Zb¯bnj 12.2 68.9 117.0 0.0 1.4 0.2

W W nj 82.8 89.0 174.8 0.0 0.0 0.0

W Znj 162.4 252.0 409.2 0.6 0.4 0.5

ZZnj 3.8 13.3 12.9 0.0 0.5 0.1

W W W nj 31.9 30.1 64.8 0.9 0.0 0.0

Table 4: Number of ℓ±±jj events at LHC for 30 fb−1, at the pre-selection and selection levels. The heavy neutrino signal is evaluated assuming mN = 60 GeV and coupling (a) to the muon, VµN = 0.01; (b) to the electron, VeN = 0.01; (c) to both, VeN = 0.01 and VµN = 0.01.

µ±µ± e±e± µ±e±

N (a) 10.0σ − −

N (b) − 0.54σ −

N (c) 4.9σ 0.28σ 1.75σ

Table 5: Statistical significance of the heavy neutrino signals in the different channels, for a mass mN = 60 GeV and coupling (a) to the muon, VµN = 0.01; (b) to the electron, VeN = 0.01; (c) to both, VeN = 0.01 and VµN = 0.01.

b¯bnj, but would still improve the direct limit from L3 [32, 33] by an order of magnitude.

(b) A 60 GeV neutrino coupling only to the electron can be discovered for mixings

|VeN| ≥ 0.030, and bounds |VeN|2 ≤ 3.1(3.6) × 10−4 can be set at 90% (95%) CL if a background excess is not observed.

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The general limits for a heavy neutrino coupling to the electron and muon are displayed in Fig. 9. It is interesting to observe that the direct limit from non-observation of like- sign dileptons at LHC will be more restrictive than indirect ones from µ − e LFV processes at low energies.

0 0.01 0.02 0.03 0.04

VeN 0

2 4 6 8 10 12 14

VµN× 10-3

Significance < 5σ 90% CL limit Indirect bound

Figure 9: Combined limits on VeN and VµN, for Vτ N = 0 and mN = 60 GeV. The red areas represent the 90% CL limits if no signal is observed. The white areas correspond to the region where a combined statistical significance of 5σ or larger is achieved. The indirect limit from µ − e LFV processes is also shown.

4.3 Opposite-sign dilepton signals

In final states e±µjj the analysis is similar but the backgrounds are much larger. In particular, opposite-sign lepton pairs from b¯bnj production are much more abundant than like-sign pairs. Opposite-sign dileptons are produced from t¯tnj dileptonic decays and W+Wnj production (which is larger than W±W±nj). We assume a heavy Dirac neutrino with a mass of 60 GeV and VeN = 0.01, VµN = 0.01. A Majorana neutrino gives this signal too, but with half the cross section for the same couplings. We use the same pre-selection cuts as in the like-sign dilepton analysis but requiring instead opposite charge for the leptons. The number of signal and background events at pre- selection is collected in the left column of Table 6. At pre-selection the b¯bnj, t¯tnj and W W nj backgrounds are 7, 15 and 70 times larger, respectively, than the corresponding ones for µ±e in Table 4.

The kinematical variables useful for discriminating the signal against the back- grounds are the same as for a 60 GeV heavy Majorana neutrino in the like-sign dilepton channels. However, in this case the distributions for some backgrounds, namely t¯tnj and W W nj, are different. We have grouped backgrounds in three classes: b¯bnj, t¯tnj,

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0 20 40 60 80 100 120 pTµ1

0 0.1 0.2 0.3 0.4 0.5 0.6

Fraction of events / 5 GeV

N (60, D) bbnj ttnj Other

0 20 40 60 80

pTµ2 0

0.2 0.4 0.6 0.8 1.0

Fraction of events / 5 GeV

N (60, D) bbnj ttnj Other

0 1 2 3 4

Rµ

1j 0

0.05 0.10 0.15 0.20

Fraction of events / 0.2

N (60, D) bbnj ttnj Other

0 1 2 3 4

Rµ

2j 0

0.05 0.10 0.15 0.20

Fraction of events / 0.2

N (60, D) bbnj ttnj Other

0 1 2 3 4 5

|∆η

1

| 0

0.05 0.10 0.15 0.20

Fraction of events / 0.2

N (60, D) bbnj ttnj Other

0 1 2 3 4 5 6 7

|∆η

2

| 0

0.05 0.10 0.15 0.20

Fraction of events / 0.2

N (60, D) bbnj ttnj Other

0 20 40 60 80 100 120 140 160 180 200

pTmax 0

0.1 0.2 0.3 0.4 0.5

Fraction of events / 10 GeV

N (60, D) bbnj ttnj Other

0 20 40 60 80 100 120

pTmax2 0

0.2 0.4 0.6 0.8

Fraction of events / 5 GeV

N (60, D) bbnj ttnj Other

Figure 10: Normalised distributions of several discriminating variables for a 60 GeV Dirac neutrino and the three background classes (see the text).

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0 20 40 60 80 100 120 140 160 180 200 p/T

0 0.05 0.10 0.15 0.20 0.25 0.30

Fraction of events / 5 GeV

N (60, D) bbnj ttnj Other

0 100 200 300 400 500 600 700 800

mµµjj 0

0.05 0.10 0.15 0.20

Fraction of events / 10 GeV

N (60, D) bbnj ttnj Other

0 1 2 3 4 5

Nb 0

0.2 0.4 0.6 0.8 1

Fraction of events

N (60, D) bbnj ttnj Other

0 5 10 15

Nj 0

0.1 0.2 0.3 0.4 0.5 0.6

Fraction of events

N (60, D) bbnj ttnj Other

-1 -0.5 0 0.5 1

cos ∆φµµ 0

0.1 0.2 0.3 0.4 0.5

Fraction of events / 0.1

N (60, D) bbnj ttnj Other

-10 -5 0 5

log10LS / LB 0

0.02 0.04 0.06 0.08 0.10

Fraction of events

N (60, D) bbnj ttnj Other

Figure 11: Normalised distributions of several discriminating variables for a 60 GeV Dirac neutrino and the three background classes (see the text). The last plot corre- sponds to the log-likelihood function.

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Pre-selection Selection

N (e, µ) 593.5 14.7

b¯bnj 602000 73

c¯cnj 5750 0

t¯tnj 233135.1 0.3

tj 1003.8 0.0

W b¯bnj 927.6 0.0

W t¯tnj 197.0 0.0

Zb¯bnj 180.8 0.0

W W nj 12016.5 0.7

W Znj 412.1 0.0

ZZnj 14.2 0.0

W W W nj 131.4 0.0

Table 6: Number of µ±ejj events at LHC for 30 fb−1, at the pre-selection and selection levels. The heavy neutrino signal is evaluated assuming mN = 60 GeV and coupling to electron and muon VeN = 0.01, VµN = 0.01.

and the other backgrounds (dominated by W W nj). The distributions for the relevant kinematical variables and the log-likelihood function are collected in Figs. 10 and 11.

For event selection we require log10LS/LB≥ 2.9, yielding the number of events in the right columns of Table 6. The significance of the heavy Dirac neutrino signal is only 0.86σ. The combined limits on VeN and VµN are presented in Fig. 12. The shape of the regions is drastically different from Figs. 6 and 9 because the sensitivity in the e+ejj and µ+µjj channels is negligible, and only when N couples sizeably to both electron and muon the heavy neutrino signal is statistically significant in the µ±ejj channel.

The direct limit from non-observation of a µ±ejj excess has a similar shape as the indirect limit but it is less restrictive in all cases.

5 Estimates for Tevatron

The observability of heavy neutrino signals in like-sign dilepton channels at Tevatron seems to be dominated by the size of the signal itself. In contrast with LHC, back- grounds are much smaller. For example, the W Zjj and W W jj backgrounds have cross sections of 0.1 and 0.09 fb, respectively, with the cuts in Eq. (6). Then, it seems reasonable to estimate the total background for 1 fb−1(including b¯b) as one event. This

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